Digital or analog images, in particular in technical applications, often require processing, such as reconstructive processing, filtering, rendering, etc. In the medical field, image processing plays an important part providing a physician with better information by improving the ability to interpret images taken by medical imaging devices. An example for a medical application is Positron Emission Tomography (PET), where a short-lived radioactive tracer isotope, which decays by emitting a positron, is injected usually into the blood circulation of a living subject. After the metabolically active molecule becomes concentrated in tissues of interest, the research subject or patient is placed in the imaging scanner. The molecule most commonly used for this purpose is fluorodeoxyglucose (FDG), a sugar, for which the waiting period is typically an hour.
As the radioisotope undergoes positron emission decay, it emits a positron, the antimatter counterpart of an electron. After traveling up to a few millimeters the positron encounters and annihilates with an electron, producing a pair of gamma photons moving in almost opposite directions. These are detected in the scanning device by a detector assembly, typically a scintillator material coupled to a photomultiplier, which converts the light burst in the scintillator into an electrical signal. The technique depends on simultaneous or coincident detection of the pair of photons.
The raw data collected by a PET scanner are a list of ‘coincidence events’ representing near-simultaneous detection of annihilation photons by a pair of detectors. Each coincidence event represents a line in space connecting the two detectors along which the positron emission occurred. Coincidence events can be grouped into projections images, called sinograms. The sinograms are sorted by the angle of each view and tilt, the latter in 3D case images. Before reconstruction, pre-processing of the data is required such as, for example, correction for random coincidences, estimation and subtraction of scattered photons, attenuation correction, detector dead-time correction and detector-sensitivity correction.
Filtered back projection (FBP) has been frequently used to reconstruct images from the projections. This algorithm has the advantage of being simple and having a low requirement for computing resources, but it is characterized by high noise level and streak artifacts.
For smoother processing image of the data generated by PET scanners and other imaging devices (CT for example), iterative reconstruction methods are used. Such methods were introduced in PET technology in the early 1980's with the publishing of the Maximum Likelihood Maximization (MLEM) algorithm. However, slow convergence and inadequate computing power prevented a widespread diffusion. The introduction of the fast convergence Ordered Subset Expectation Maximization (OSEM) and the progress in computing speed made iterative algorithms the standard for clinical PET. The advantage is a better noise profile and resistance to the streak artifacts common with FBP, but the disadvantage is higher computer resource requirements. Moreover, in MLEM, OSEM and similar algorithms, the contrast recovery improves with the iteration number, but image noise also increases with the iteration number, and the balance of these two opposite parameters is commonly left to an arbitrary choice of when to stop the iterative process. Moreover, in the clinical practice, a fixed iteration number is a-priori selected and applied in all situations.
To improve an iterative process, a row-action maximum likelihood algorithm (RAMLA) has been introduced, in which the progress of iteration is damped by a relaxation parameter. The image noise and signal recovery are made to converge quickly to a solution and any farther iteration does not alter the noise level and contrast recovery. However, the choice of the relaxation parameter and its update law is again arbitrary and the result is equivalent to stopping the iterative algorithm at an arbitrary point.
In other technical fields of image processing, the optimal post smoothing, for example, of an astronomical image or of a planar scintigraphic image has been investigated and it has been found that a confidence test can be used in order to define the size of a local smoothing kernel. In these applications, the balance has to be found between large kernels which provide smooth images and small kernels which minimize the bias.